290 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS ured may be derived from the ends, where the shear velocities vary from low values (zero at the center of the bottom) to maximum at the outside diameter of the bob. Again, a distribution of shear velocities is obtained, and the associated distribution of viscosities makes the measured value unreliable. A number of methods have been devised to eliminate this problem, which was recognized even by Couette in his original instrument. So-called "guard rings" were installed at the top and bottom of the bob as shown in Fig. 4. They absorb the torque imparted to these areas by the rotating cup and restrict the measurement to the annular space between cup and bob. Although effective in their purpose, the guard rings are compli- cated to construct and adjust and are consequently generally avoided. A simple and elegant method for compensating for these end anomalies was introduced by Mooney and Ewart (12). Instead of employing cup and bobs which are parallel at their ends, conical bottoms are employed, having different angles from each other as shown in Fig. 5. These angles are calculated in such a way that the rate of shear between them is the same as that between the cylindrical surfaces of the viscometer. The error arising from the top end of the bob can readily be avoided by filling the viscometer only part way, and thus eliminating material from this point. Wr tan • CONE AND PLATE VISCOMETER Figure 6.

ROTATIONAL METHODS OF FLOW MEASUREMENTS 291 (]]ONE AND PLATE VISCOMETER It is perhaps somewhat surprising that this simple expedient of conical bottoms was not employed earlier. Perhaps even more surprising is the fact that this principle was not used until recently in commercial viscom- eters to eliminate shear velocity distributions in a simple rotational in- strument. Thus, by employing a plain bottom plate and a bob of low angle, while simultaneously eliminating the cylindrical portion of the in- strument, the cone and plate viscometer illustrated in Fig. 6 is evolved. Properly constructed, this instrument has the feature of providing a con- stant shear gradient throughout its measuring surfaces, since: dv rl4/ - K (10) dr - r tan a where////is the rotational velocity of cone or plate, a is the angle between the two surfaces and K is a constant. It will be noted that a requirement of the geometry of this system for successful operation is that the apex of P TRANSLATIONAL VISCOMETER Figure 7.